New analytic solutions with thrust tangential or perpendicular to the flight direction: a class of generalized parabolas

Abstract

This study presents the orbital dynamics of a spacecraft moving along a planar trajectory in the shape of a generalized parabola. The analysis method used is inspired by Siacci’s theorem, since the acceleration is decomposed into a central component and a tangential component. This allows us to obtain the expression for the continuous thrusts of the spacecraft as a function of the orbital distance, in cases where the thrust is parallel or perpendicular to the trajectory. Numerous original solutions are presented, which are then applied, for example, to the organization of orbital rendezvous or to suggest alternatives to the classical Hohmann transfer. In the latter case, \(\Delta v\) and flight time comparisons are carried out, in particular with simulations of Earth-Saturn transfers.